In contrast, other methods discard important information encoded in higher dimensions. This is well-understood for linear methods like PCA that focus on explaining global variances, as this comes at the expense of distorting fine grained structures in data [1]} (Fig. S2A-S2C). In practice, this means that PCA is able to find some global contrasts in our data, like the major differences in metabolic capabilities between Actinobacteria and \(\gamma \) -proteobacteria (Fig. S2B). However, the method is inherently unable to capture structures that lie near nonlinear submanifolds. As a consequence, fine details like intra-class differences in metabolic traits are obfuscated (e.g., Fig S2C).
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